Geometry Review. Multiple Choice Identify the choice that best completes the statement or answers the question.

Transcription

1 Geometr Review Multiple hoice Identif the choice that best completes the statement or answers the question. 1. Tell whether the ordered pair (5, 3) is a solution of the sstem. a. es b. no 2. Solve Express our answer as an ordered pair. a. ( 3, 2) c. ( 4, 1) 3 b. ( 2, 3) d. ( 8, 3) 3 3. Solve. Express our answer as an ordered pair. a. (8, 4) c. ( 2, 4) b. (4, 8) d. (4, 8) 4. Name two lines in the figure. W T R a. and T c. b. WR and TR d. and and 5. Draw and label a pair of opposite ras and. a. c. H F G H F G b. G F H d. H F 6. Find the length of. G a. = 7 c. = 7

2 b. = 9 d. = 8 7. D is between and E. =, =, and DE = 27. Find E. D E 4 x x a. E = 17.5 c. E = 105 b. E = 78 d. E = The map shows a linear section of Highwa 35. Toda, the Ybarras plan to drive the 360 miles from Springfield to Junction it. The will stop for lunch in Roseburg, which is at the midpoint of the trip. If the have alread traveled 55 miles this morning, how much farther must the travel before the stop for lunch? S 55 mi X R 360 mi a. 125 mi c. 180 mi b. 145 mi d. 305 mi 9. K is the midpoint of. and. Find JK, KL, and JL. a. JK = 1, KL = 1, JL = 2 c. JK = 12, KL = 12, JL = 6 b. JK = 6, KL = 6, JL = 12 d. JK = 18, KL = 18, JL = Find the measure of. Then, classif the angle as acute, right, or obtuse. J D O a. m ; obtuse c. m ; acute b. m ; obtuse d. m ; obtuse 11. m and m. Find m.

3 I L J K a. m c. m b. m d. m 12. bisects, m, and m. Find m. a. m = 22 c. m = 40 b. m = 3 d. m = Tell whether and are onl adjacent, adjacent and form a linear pair, or not adjacent. F G a. not adjacent b. onl adjacent c. adjacent and form a linear pair 14. Find the measure of the complement of, where m 15. Find the measure of the supplement of, where m 16. n angle measures 2 degrees more than 3 times its complement. Find the measure of its complement. 17. Find the perimeter and area of the figure. 6 6x x + 8

4 a. perimeter = ; area = b. perimeter = ; area = c. perimeter = ; area = d. perimeter = ; area = 18. The rectangles on a quilt are 2 in. wide and 3 in. long. The perimeter of each rectangle is made b a pattern of red thread. If there are 30 rectangles in the quilt, how much red thread will be needed? a. 10 in. c. 180 in. b. 150 in. d. 300 in. 19. Find the coordinates of the midpoint of with endpoints (1, 6) and M(7, 5). a. (3, 1) c. (4, 1 2 ) b. (8, 1) d. (4 1 2, 1 2 ) 20. M is the midpoint of, has coordinates ( 6, 6), and M has coordinates (1, 2). Find the coordinates of N. a. (8, 10) c. ( 2 1, 2) 2 b. ( 5, 4) d. (8 1 2, 91 2 ) 21. Find D and EF. Then determine if. E D x 1 F a.,, b.,, c.,, d.,, 22. Use the Distance Formula and the Pthagorean Theorem to find the distance, to the nearest tenth, from T(4, 2) to U( 2, 3). a. 1.0 units c. 0.0 units b. 3.4 units d. 7.8 units 23. Give an example of corresponding angles.

5 a. and c. and b. and d. and 24. Identif the transversal and classif the angle pair and. n m l a. The transversal is line l. The angles are corresponding angles. b. The transversal is line l. The angles are alternate interior angles. c. The transversal is line n. The angles are alternate exterior angles. d. The transversal is line m. The angles are corresponding angles. 25. Find m. >> xº (3x - 70)º >> a. m = 40 c. m = 35 b. m = 45 d. m = Find m.

6 R >> S (3x)º T U (4x 24)º >> V a. m = c. m = b. m = d. m = 27. In a swimming pool, two lanes are represented b lines l and m. If a string of flags strung across the lanes is represented b transversal t, and x = 10, show that the lanes are parallel. (3x + 4)º l (4x 6)º t m a. ; The angles are alternate interior angles and the are congruent, so the lanes are parallel b the lternate Interior ngles Theorem. b. ; The angles are alternate interior angles, and the are congruent, so the lanes are parallel b the onverse of the lternate Interior ngles Theorem. c. ; The angles are corresponding angles and the are congruent, so the lanes are parallel b the onverse of the orresponding ngles Postulate. d. ; The angles are same-side interior angles and the are supplementar, so the lanes are parallel b the onverse of the Same-Side Interior ngles Theorem. 28. Use the slope formula to determine the slope of the line.

7 Time (h) Distance (ft) Distance (ft) x a. 0 c. 3 2 b. 2 3 d. undefined 29. Milan starts at the bottom of a 1000-foot hill at 10:00 am and bikes to the top b 3:00 PM. Graph the line that represents Milan s distance up the hill at a given time. Find and interpret the slope of the line. a b x Time (h) The slope is 200, so Milan traveled 200 feet per hour x Time (h) c. The slope is, so Milan traveled feet per hour x Distance (ft) The slope is, so Milan traveled feet per hour.

8 Time (h) d x Distance (ft) The slope is, so Milan travels feet per hour. 30. Use slopes to determine whether the lines are parallel, perpendicular, or neither. a. neither c. parallel b. perpendicular 31. Write the equation of the line with slope 2 through the point (4, 7) in point-slope form. 32. Determine whether the lines and are parallel, intersect, or coincide. a. intersect c. parallel b. coincide 33. ppl the transformation M to the triangle with the given vertices. Identif and describe the transformation. M: (x, ) (x 6, + 2) E(3, 0), F(1, 2), G(5, 4) a. 7 c. 7 E' F' 7 7 x E E' 7 7 x E G' F F' F G G' G 7 This is a translation 6 units left and 2 units up. This is a translation 6 units left. 7

9 b. 7 E' d. 7 F' F G' 7 7 x 7 This is a translation 2 units left and 6 units up. E G 7 7 x F' E' G' 7 F This is a translation 6 units left and 2 units down. E G 34. ppl the transformation M to the polgon with the given vertices. Identif and describe the transformation. M: (x, ) ( x, ) ( 3, 6), ( 3, 1), (1, 1), D(1, 6) a. 7 D c. 7 D Z Y 7 7 x 7 X Y 7 x W X 7 W 7 Z This is a rotation of 180 about the origin. This is a reflection over the x-axis.

10 b. 7 D d. 7 D X W 7 Y X 7 x 7 7 x Y Z Z 7 W 7 This is a rotation of 180 about the origin. This is a rotation of 90 clockwise about the origin. 35. Determine whether triangles and are congruent. 6 G E F 6 6 x P Q 6 R a. The triangles are congruent because can be mapped to b a reflection:. b. The triangles are congruent because can be mapped to b a rotation:. c. The triangles are congruent because can be mapped to b a reflection:. d. The triangles are congruent because can be mapped to b a rotation:. 36. Prove that the triangles with the given vertices are congruent. (3, 1), (4, 5), (2, 3) D( 1, 3), E( 5, 4), F( 3, 2) a. The triangles are congruent because can be mapped onto b a rotation:, followed b a reflection:.

11 b. The triangles are congruent because can be mapped onto b a reflection:, followed b a rotation:. c. The triangles are congruent because can be mapped onto b a translation:, followed b another translation:. d. The triangles are congruent because can be mapped onto b a rotation:, followed b a reflection:. 37. Tell whether the transformation appears to be a reflection. Explain. a. Yes; the image appears to be flipped across a line. b. No; the image does not appear to be flipped. 38. Reflect a figure with vertices across the x-axis. Find the coordinates of the new image. a. b. c. d. 39. Find the coordinates of the image of the point when it is reflected across the line. 40. Tell whether the transformation appears to be a translation. Explain. a. Yes; all of the points have moved the same distance in the same direction. b. No; not all of the points have moved the same distance. 41. Find the translation of the triangle along.

12 v 42. Translate the triangle with vertices along the vector. Find the coordinates of the new image. a. b. c. d. 43. Rotate with vertices R(4, 1), S(5, 3), and Q(3, 1) b 90 about the origin.

13 a. S' Q' c. R' S S Q R' Q R x Q' R x S' b. d. S S' S Q Q' Q R x R' R x Q' R' S' 44. The point is rotated about point and then reflected across the line. Find the coordinates of the image. 45. Tell whether the transformation appears to be a dilation. Explain. a. Yes; the figures are similar, and the image is not turned or flipped. b. No; the figures are not similar. 46. Given the rectangle and the center of dilation P, which of the following is a dilation with a scale factor of 2?

14 P a. c. P P b. d. P P 47. On a sketch of a mural, 3 inches represents one foot in the mural. door in the sketch is 2 inches wide b 5 inches high. What is the perimeter of the door in the mural expressed in inches? a. 4 in. c. 20 in. b. 8 in. d. 56 in. 48. triangle with vertices,, and is given. Which of the following is the image of the triangle under a dilation with a scale factor of centered at the origin? x

15 a. ' 12 c ' ' 4 ' x ' x ' 8 12 b. 12 d. 12 ' ' ' x x 4 ' ' 8 12 ' _06_GE_03 Transformations: lassifications of In the diagram below, under which transformation will be the image of? a. rotation c. translation b. dilation d. glide reflection _06_GE_07 Parallel and Perpendicular Lines What is an equation of the line that passes through the point and is perpendicular to the line whose equation is?

16 _06_GE_08 Transformations: ompositions of fter a composition of transformations, the coordinates,, and become,, and, as shown on the set of axes below. Which composition of transformations was used? _06_GE_18 Solid Geometr: Lines and Planes in Space Point P is on line m. What is the total number of planes that are perpendicular to line m and pass through point P? a. 1 c. 0 b. 2 d. infinite _06_GE_19 Midpoint Square LMNO is shown in the diagram below. What are the coordinates of the midpoint of diagonal? _06_GE_26 Parallel and Perpendicular Lines

17 Which equation represents a line perpendicular to the line whose equation is? _08_GE_01 Parallel Lines: ngles Involving ased on the diagram below, which statement is true? _08_GE_02 onstructions The diagram below shows the construction of the bisector of. Which statement is not true? _08_GE_06 Transformations: lassifications of Which transformation produces a figure similar but not congruent to the original figure? _08_GE_08 Transformations: ompositions of On the set of axes below, Geoff drew rectangle D. He will transform the rectangle b using the translation and then will reflect the translated rectangle over the x-axis.

18 What will be the area of the rectangle after these transformations? a. exactl 28 square units c. greater than 28 square units b. less than 28 square units d. It cannot be determined from the information given _08_GE_09 Parallel and Perpendicular Lines What is the equation of a line that is parallel to the line whose equation is? _08_GE_10 Midpoint The endpoints of are and. What are the coordinates of the midpoint of? _08_GE_17 Parallel and Perpendicular Lines What is the slope of a line perpendicular to the line whose equation is? _08_GE_19 Distance If the endpoints of are and, what is the length of? b. 2 d _08_GE_27 Solid Geometr: Lines and Planes in Space If two different lines are perpendicular to the same plane, the are a. collinear c. congruent b. coplanar d. consecutive 64. Triangle has vertices,, and. Under a translation,, the image point of, is located at. Under this same translation, point is located at 65. Line k is drawn so that it is perpendicular to two distinct planes, P and R. What must be true about planes P and R?

19 a. Planes P and R are skew. b. Planes P and R are parallel. c. Planes P and R are perpendicular. d. Plane P intersects plane R but is not perpendicular to plane R. 66. The diagram below illustrates the construction of parallel to through point P. Which statement justifies this construction? 67. The figure in the diagram below is a triangular prism. Which statement must be true? 68. What is the equation of a line that passes through the point and is parallel to the line whose equation is? 69. Line segment has endpoints and. What are the coordinates of the midpoint of?

20 70. polgon is transformed according to the rule:. Ever point of the polgon moves two units in which direction? a. up c. left b. down d. right 71. In the diagram below of, D is a point on,,, and. The length of could be a. 5 c. 19 b. 12 d The lines and are a. parallel c. the same line b. perpendicular d. neither parallel nor perpendicular 73. What is the slope of a line perpendicular to the line whose equation is? 74. In the diagram below, under which transformation is the image of? 75. Triangle is similar to triangle DEF. The lengths of the sides of are 5, 8, and 11. What is the length of the shortest side of if its perimeter is 60? a. 10 c. 20 b d. 27.5

21 76. Square D has vertices,,, and. What is the length of a side of the square? Numeric Response 77. Find the value of x so that. (6x + 5)º m (5x - 12)º n 78. Under a rotation about the origin, the point is mapped to the point. What is the measure, in degrees, of the angle of rotation? Short nswer _06_GE_29 Medians, ltitudes, isectors and Midsegments In the diagram of below,,, and. Find the perimeter of the triangle formed b connecting the midpoints of the sides of _06_GE_31 Parallel and Perpendicular Lines Find an equation of the line passing through the point _08_GE_31 Parallel and Perpendicular Lines Write an equation of the line that passes through the point. and parallel to the line whose equation is and is parallel to the line whose equation is

22 Geometr Review nswer Section MULTIPLE HOIE D D D D D D D

23 D D D D D D NUMERI RESPONSE SHORT NSWER

24 81.